I am a research mathematician. In my field (abstract algebra, computational group theory), a sum or some such notation is like the most trivial of trivial things in terms of notation. There are a few things like sums that could in theory be made to "look more like what a computer programmer would expect", but that'd be just a tiny corner of it.
And if you think about how summation would look in Lisp or APL (which some smart people use to this day), I am not even convinced your argument for the "sum function" notation being superior holds in general.
And if you think about how summation would look in Lisp or APL (which some smart people use to this day), I am not even convinced your argument for the "sum function" notation being superior holds in general.